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arXiv · 2008.01130

On the Bernstein-von Mises theorem for the Dirichlet process

Kolyan Ray·Aad van der Vaart
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Abstract

We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random variables and functions of bounded variation, we strengthen this result to hold for all real numbers. This last result is proved via an explicit strong approximation coupling inequality.

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Kolyan Ray, Aad van der Vaart. 2020-08-03. On the Bernstein-von Mises theorem for the Dirichlet process. https://doi.org/10.1214/21-ejs1821

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